Submanifolds of symplectic manifolds with contact border

TL;DR

This paper constructs symplectic submanifolds with contact boundary within symplectic manifolds, characterizes their topology, and discusses potential applications in symplectic and contact geometry.

Contribution

It introduces a method to construct symplectic submanifolds with contact boundary and provides a topological characterization via a relative Lefschetz hyperplane theorem.

Findings

Boundary of submanifolds is a contact submanifold

Constructed submanifolds are topologically characterized

Applications in symplectic and contact geometry are discussed

Abstract

We construct symplectic submanifolds of symplectic manifolds with contact border. The boundary of such submanifolds is shown to be a contact submanifold of the contact border. We also give a topological characterization of the constructed submanifolds by means of a ``relative Lefschetz hyperplane Theorem''. We sketch some of the applications of the results.